Serialnumber of imac

i need to find out my serialnumer of my imac and yes ive seen the apple page where they tell you where to find it. i just got some problems:
the case is gone.
the imac is broke, so i can find it there aswell.
the number on the imac itself is so ********* up that u cant read it anymore
and i can find the bill anymore.

i try to find it with my apple-id but there its not
the only things i got left is the packing list and my ordernumber.
i try to look with the ordernumber but i could find it because i bought it i 2008. any help?
thanks

 

thanks, i ll have to go to an apple store in germany, i just lived in texas for a year